Deriving electromagnetic fieldfor point charge

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SUMMARY

The discussion focuses on the derivation of the electromagnetic field for point charges as presented in Griffith's "Introduction to Electrodynamics" (page 437). A participant identifies an error in their calculation involving the expression for the gradient of a vector field, specifically the application of the triple cross product rule. The correct formulation includes a crucial minus sign that was initially overlooked. This correction is essential for accurate electromagnetic field derivation.

PREREQUISITES
  • Understanding of vector calculus, particularly the gradient and cross product operations.
  • Familiarity with Griffith's "Introduction to Electrodynamics" and its notation.
  • Knowledge of electromagnetic theory, specifically the behavior of point charges.
  • Experience with mathematical derivations in physics.
NEXT STEPS
  • Review the triple cross product rule in vector calculus.
  • Study the derivation of electromagnetic fields for various charge distributions.
  • Explore advanced topics in electrodynamics, such as Maxwell's equations.
  • Practice solving problems related to point charges and their fields using Griffith's framework.
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching vector calculus, and researchers focusing on theoretical physics and electromagnetic field theory.

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Hi all,

I was going through the derivation for the electromagnetic field of point charges by Griffith(Introduction to electrodynamics page 437).

I'm missing minus sign somewhere:

The book says that:\nabla(\vec{n}\cdot\vec{v})=\vec{a}(\vec{n}\cdot \nabla tr)+\vec{v}-\vec{v}(\vec{v}\cdot\nabla tr)-\vec{n}\times(\vec{a}\times \nabla tr)+\vec{v}\times (\vec{v}\times \nabla tr)

Using the rule for triple cross products gives:

\vec{v}+(v^{2}-\vec{n}\cdot\vec{a})\nabla tr

However is should be:

\vec{v}+(-v^{2}+\vec{n}\cdot\vec{a})\nabla tr


I'm sure I am missing something.

Thanks
 
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oh I've got it. Forgot the minus sign in the triple cross product rule :$
 

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